In order to evaluate the decoherence for ensembles of NV centers we need to integrate over a distribution of various \(\kappa \)  and \(\tau _{c}\) . With a full derivation available in Ref. [1]}, the result for the case of dipolar couplings to a spin bath results in the same expression as \(T_{2,single}^{*}\)  albeit with the stretched exponential parameter \(p=1\)  and \(T_{2,ensemble}^{*}=1/\kappa _{ens}\) .
